On the eigenvalues of firefly graphs

The sharp upper bounds and the sharp lower bounds of the largest‎ ‎eigenvalues $\lambda_1$‎, ‎the least eigenvalue $\lambda_n$‎, ‎the second largest eigenvalue $\lambda_2$‎, ‎the spread and the‎ ‎separator among all firefly graphs on $n$ vertices are determined‎.